main principle of the proposed method in the case of using. Histogram Matching based on Gaussian Distribution. (HMGD). And in order to automatically detect ...
International Journal of Affective Engineering Vol.14 No.2 (Special Issue) pp.85-93 (2015)
Special Issue on 2013 ICBAKE (International Conference on Biometrics and Kansei Engineering), Part 2
ORIGINAL ARTICLE
Automated Color Image Arrangement Method Based on Histogram Matching – Investigation of Kansei impression between HE and HMGD – Yusuke KAWAKAMI*, Tetsuo HATTORI*, Haruna MATSUSHITA*, Yoshiro IMAI*, Hiromichi KAWANO** and R.P.C. Janaka Rajapakse*** * Graduate School of Engineering, Kagawa University, 2217-20 Hayashi-cho, Takamatsu-shi, Kagawa 761-0396, Japan ** NTT Advanced Technology, 1-19-18 Naka-machi, Musashino-shi, Tokyo 180-0006, Japan *** Taiwan National University of Arts, 66 Daci-village, Guantian-district, Tainan 72045, Taiwan
Abstract: We propose a novel color image arrangement method using an elastic transform based on histogram matching on some kinds of axes. The axes include the lightness axis and Principal Component (PC) axes obtained from Principal Component Analysis (PCA) in the RGB three-dimensional vector space that is an attribute space of color image. In this paper, we mainly present the principle of its automated color arrangement method especially based on Histogram Matching based on Gaussian Distribution (HMGD). Then, in order to detect the single-peak of histogram, we propose the method based on the curvature computation for the cumulative histogram. Furthermore, we conducted a questionnaire survey in order to investigate compare the changes in the feeling impression at the time of performing between Histogram Equalization (HE) processing and HMGD processing. As the result, we verify that where we perform HMGD processing to the images which have single-peak-histogram the feeling impression of images are improved. Keywords: Automated color arrangement, Elastic transform, Histogram matching
histogram, Kansei impression will be improved by using HMGD. Additionally, we conduct a questionnaire survey in order to investigate compare the changes in the feeling impression at the time of performing between Histogram Equalization (HE) processing and HMGD processing. Then, we verify that HMGD is effective automated color image arrangement method for single-peak-histogram image.
1. INTRODUCTION Automated image processing for enhancement and/or arrangement of color images has been more familiar to us according to the spreading of Digital Camera, Smart Phone, DVD, etc. [1-3]. However, we consider that the research on the automated arrangement method that brings about good sensibility effect (or Kansei effect) is still on the way to practical use. In this paper, we propose a novel color image arrangement method using an elastic transform based on histogram on some kinds of axes [4-6]. As for the axes, there are lightness axis and principal component one that can be obtained by Principal Component Analysis (PCA) in the RGB three-dimensional vector space that is an attribute space of color image. Especially, we explain the main principle of the proposed method in the case of using Histogram Matching based on Gaussian Distribution (HMGD). And in order to automatically detect the number of peaks of histogram, we propose the method based on the curvature computation for the cumulative histogram, because HMGD processing is transformation from original histogram to Gaussian distribution histogram. That is, we thought if the original image has single peakedness
Received 2014.03.04 Accepted 2014.12.15
2. ELASTIC TRANSFORM BASED ON HISTOGRAM MATCHING 2.1 Principle We describe the principle of histogram based elastic transform in the following. Let f(x) and g(y) be two probabilistic density functions on real variables x and y, respectively. The probabilistic density function (PDF) is corresponding to histogram of gray level image. However, the PDF is defined on discrete variable. In addition, let y = φ (x) be a continuous and monotonous increase function between variables x and y as shown in Figure 1. In addition, let value of x be the range from 0 to L. Accordingly, variable y ranges from 0 to φ (L). Let P mean the probability. From the above definitions and Figure1,
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International Journal of Affective Engineering Vol.14 No.2 (Special Issue)
we have Equation (1)-(3). (1) (2)
(3)
From Equation (3), we obtain Equation (4) and (5) because y0 = φ (x0) and y0 + dy = φ (x0 + dx). (4) (5)
Figure 1: Continuous and monotonous increase function y=φ (x) and probabilistic density functions f(x) and g(y) (Conceptual image of Histogram Matching (HM)).
Thus, if we know the y = φ (x) and g(y), then we have the f (x). Using the above equations, we derive the principle of Histogram Equalization (HE). Let φ (x) be defined by Equation (6). (6) Since φ ′(x) = Mf(x), according to Equation (5), we derive the following Equation (7). (7) Therefore, we understand that if we take the transform function as Equation (6), g(y) becomes uniform distribution. It corresponds to the HE processing, which means that function defined by cumulative histogram transforms the original PDF into the uniform one. Inversely, if we define the transform function φ (x) as an integral of desired PDF f(x), e.g. Gaussian distribution, we can obtain the desired PDF using the φ (x) and the uniform distribution such as shown in Figure 2 (a). The abovementioned theory means that, if we combine the both transform, we can obtain the transformation from an original PDF to a desired one. This means that an image with original PDF can be transformed into another image with desired PDF. We consider that it is the principle of the Histogram Matching (HM) [4]. Figure 2 (b) shows the conceptual image of Histogram Matching based on Gaussian Distribution (HMGD).
(a) Conceptual image of Histogram Equalization (HE)
2.2 Elastic Transform on Axis We can choose the abovementioned transform such as Histogram Equalization (HE) and Histogram Matching (HM) on arbitrary axis (for example, principal component axis) in the color attribute space (RGB space) as shown in Figure 3. For example, in the case where the HE processing on the lightness axis is applied, the HE brings about image enhancement by contrast stretching.
(b) Conceptual image of Histogram Matching based on Gaussian Distribution (HMGD) Figure 2: Conceptual image of the transform from uniform distribution (PDF) to the desired one.
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International Journal of Affective Engineering Vol.14 No.2 (Special Issue) Automated Color Image Arrangement Method Based on Histogram Matching
Therefore we consider that the HMGD processing is more moderate than HE processing. Moreover, we have considered that the Gaussian distribution used in HMGD processing have single peakedness. As the result, because HMGD processing use one reference histogram, we consider that the original image histogram has to be almost single peakedness. So we achieved automation HMGD processing by detecting the number of peakedness of the original image histogram by using curvature computation. The specific method is as follows.
Figure 3: Conceptual image of histogram based elastic transform on arbitrary axis in RGB space.
(a) Original
(b) The lightness axis
• Step 1: Detect the number of peakedness histogram of the input image. Proceed to Step 2 if the histogram of it is single. Otherwise quit. • Step 2: Perform HMGD processing to the input image. • Step 3: Output the HMGD processing image.
(c) PC axis
Figure 4: Example of HE on the lightness axis and PC axis
(a) Original
(b) HE
2.3 Curvature Computation for Detection of Single Peakedness Histogram In the previous section, we describe the method of automated HMGD processing. So in this section, we describe how we detect the histogram peakedness by using curvature. Let y be a function with respect to x, the definition of the curvature R is given by Equation (8).
(c) HMGD
Figure 5: Example of the results by HE and HMGD.
In addition, in the case of HE on a principal component axis in RGB space, we guess that the contrast stretching will be done along to a certain tone of color. Figure 4 shows examples of the HE on the lightness axis and Principal Component (PC) axis. And, in the case where the HM processing on the lightness axis is applied, the HM brings about lightness level arrangement by histogram transform function. If we set the probabilistic density function (PDF) of Gaussian distribution up as transformation function, original histogram distribution is approximated to Gaussian distribution histogram. We named “Histogram Matching based on Gaussian Distribution (HMGD)” the HM of this case. Figure 5 shows resultant examples of the HE and HMGD on the lightness axis. As shown in Figure 5 (b), the wrinkles of men suits are blacked out. And, not only curtain wrinkles are too highlighted, but also overexposure can be found in the window frame and the wall of the room. But in Figure 5 (c), it can be seen clearly shadow of wrinkles of clothes of men. In addition, shades of wrinkles in the curtain are suppressed, and the detail of window frame is clear.
(8)
Let g(x) be a Gauss density function with variance σ 2 and average a. And also let g(x) be representing a histogram of input image whose pixel values from 0 to L. That is, (9) In Equation (9), K means a coefficient that satisfies the following Equation (10). (10) Let y = f(x) be a function representing the cumulative histogram. Then f(x) can be represented Equation (11). Since , it can be described as Equation (12).
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International Journal of Affective Engineering Vol.14 No.2 (Special Issue)
3. INVESTIGATION (11) We conducted a questionnaire survey in order to investigate compare the changes in the Kansei impression at the time of performing between HE processing and HMGD processing. The examinees are 36 university students in the age of early 20s. We have given some questions about their feeling impression of 10 pairs of image. Figure 7 and Figure 8 [9] show the original images, HE processing images, and HMGD processing images, in which used the investigation.
(12) By the same way,
(13)
Hence, we obtain the following Equation (14) and we can approximate to Equation (8).
(14)
(a) Image 1: Original image (left), HE processing image (center), HMGD processing image (right)
The curvature R varies the sign according to the value of x: (x 0, (x = a) R = 0, (x > a) R
